1. Yukie Maeda（前田幸重） Univ. of Miyazaki（宮崎大学）
Effects of three-nucleon force and the experimental study via the few-nucleon systems
Yukie Maeda（前田幸重）
Univ. of Miyazaki（宮崎大学）
The 9th Japan-China Joint Nuclear Physics Symposium (JCNP 2015)
Osaka University, Nov

2. Outline History Experimental study by few-nucleon systems
Three-body problem
Three-nucleon force (3NF) effects in the nuclear physics
Experimental study by few-nucleon systems
nucleon – deuteron (N+d) elastic scattering
proton – deuteron (pd) breakup reaction
4 body system (tetra neutron & p-3He)
New theoretical study
Summary

3. Lao zi (老子) said in “Tao-te Ching (道德经)”;
The Tao produced One;
One produced Two;
Two produced Three;
Three produced All things.
[Chapter 42]

4. One produced Two [Nucleon – Nucleon potentials]
One pion exchange
Yukawa (1935)
Phenomenological NN potential ( )
CDBonn, AV18, Nijmegen I, II, 93
The c2/datum ~ 1 for the fit of about 4500 np & pp scattering data
Cross sections, Spin observables @ E < 350 MeV
Next : Two produced Three ?
Many body interactions are needed ?
S. Aoki et al. PTEP 2012 (2012) 01A105

5. It will be found that the use of two-body interactions is an excellent approximation for electronic motions in atomic systems, but a relatively poor one for the heavy particles in nuclei.
The three-body effect is very small in pure s-state. If there is a considerable amount of p- and higher states in triton, the three-body force becomes important.

6. Two pion exchange 3NF 2p-exch. + D-isobar Tucson-Melbourne (TM)
Fujita-Miyazawa (1957)
Tucson-Melbourne (TM)
Urbana-IX (UIX)
a,b,c,d ; determined by pN scattering data
<- FM type
A, U0 ; determined by fitting B.E.(3H) & nuclear matter density

7. Two produced Three [Binding Energy of 3H]
Faddeev calculations
based on phenomenological NN pot.
under bind about 0.5 – 1 MeV -> explained by introducing 3NF !
parameter of 3NF is determined to reproduce B.E. of 3NS.
Next : Three produced All things ?
Many body systems require 3NF ?

8. Three produced All things ? [Neutron drip line]
T. Otsuka et al., Phys. Rev. Lett. 105 (2010)
Drip line of oxygen is near from the stability line (oxygen anomaly)
3NF provides repulsive interactions between valence neutrons.

9. Three produced All things ? [Neutron Star]
S. Gandolfi et al., PRC 85 (2012)
NASA
Many data about M ~ 1.4 Msolar
Recent accurate data of M = 2 Msolar
Short-range term of 3NF plays a key role in the high-density EOS.
Mass-to-radii correlation is sensitive to the detail of 3NF.

10. Three produced All things ? [3N scattering states]
3NF is essential for the nuclear physics.
Phenomenological NN ; c2/datum ~ 1 for the fit of 4500 data !!
3NF potentials ; should be studied comprehensively.
Experiments of the nucleon-deuteron (Nd) scattering at the intermediate energy region
Cross sections & spin observables at various energies
Comparison with the Faddeev calculations
p+d & n+d elastic
pd breakup
pd capture

12. By Courtesy of K. Sekiguchi (Tohoku Univ.)

13. By Courtesy of K. Sekiguchi (Tohoku Univ.)

14. NN
NN+TM’
AV18+UR

15. pd inclusive/exclusive breakup meas. @ RCNP
Neutron TOF N0 p
LAS p
Grand Raiden
inclusive D(p,p’) & exclusive n p
inclusive

16. D(p,p)pn & D(p,n)pp inclusive breakup
FSI
FSI
FSI
D(p,p)pn
@ 250MeV
S. Kuroita et al.
(Kyushu Univ.)　
D(p,n)pp
@ 170MeV
Y.M. et al.

17. d(p,p1p2) exclusive breakup reaction @ 250MeV
q1= (qn=) 40 deg,
q2~ 67 deg, Y.M. et al.
q1=15 deg, E1~150 MeV, S. Kuroita et al.
Discrepancies are large at small q2 (small En)
Data around FSI region is well reproduced

18. Summary of Nd scattering (isospin T=1/2)
Nd scatterings are good probe for the study of 3NF
Dynamics of 3NF (Energy & Spin dependence)
Some data is well reproduced by NN + 3NF
Cross sections & Ay of elastic E < 150 MeV
Exclusive breakup reactions in FSI kinematical configurations
Some data is not reproduced by NN + 3NF
Elastic & breakup higher energy region
Tensor spin observables of elastic scattering
What is missing ?
Relativistic effects, Coulomb force
Higher order (3p-ring etc) 3NF, heavier meson (r, s) exchange 3NF
Isospin T = 3/2 components
NEXT topic

19. 3NF of T=3/2 components in the Light Nuclei
J. Carlson et al., Rev. Mod. Phys. 87 (2015) 1067.
Illinois-7 (IL7) ; parameters are determined by fitting of g.s. & excited states of light nuclei
Strong isospin dependence
How we can get almost direct information of T = 3/2 3NF components by 3 or 4 body systems?

20. Tetra-neutron (4n) Search
By Courtesy of K. Kisamori (RIKEN)
Tetra-neutron (4n) Search
SHARAQ06 Collaboration
S. Shimoura, K. Kisamori
1 CNS, The University of Tokyo
K. Kisamori2, S. Shimoura, H. Miya2,
S. Michimasa, S. Ota, T. Fujii, S. Go,
S. Kawase, M. Kobayashi, Y. Kubota2,
C. S. Lee2, Y. Sasamoto, M. Takaki,
L. Tang, H. Tokieda, K. Yako,
R. Yokoayama
2 RIKEN Nishina Center
H. Baba, M. Dozono, N. Fukuda,
N. Inabe, D. Kameda, T. Kubo,
M. Kurata-Nishimura, H. Sakai,
M. Sasano, H. Sato, Y. Shimizu,
H. Suzuki, H. Takeda, S. Takeuchi,
T. Uesaka, Y. Yanagisawa
3 Kyoto University
T. Kawabata, T. Baba, M. Tsumura
4 RCNP Osaka University
E. Ideguchi, K. Miki, A. Tamii
5 CYRIC, Tohoku University
M. Itho
6 Tokyo Institute of Technology
Y. Kondo
7 University of Miyazaki
Y. Maeda
8 the University of Tokyo
T. Nishi
9 NSCL, Michigan State University
S. Noji, A. Stolz,
10 Kyushu University
S. Sakaguchi2
11 IPN Orsay
D. Beaumel, M. Assie, F. Hammache
12 National Institute of Radiological Sciences
H. Matsubara
part of collaborators

21. Design of the Experiment
By Courtesy of K. Kisamori (RIKEN)
Design of the Experiment
Reaction : 4He(8He,8Be)4n
Reaction with unstable beam
→ 4n system with small momentum transfer (almost recoil less condition) 4n
8He
8Be
4He
Compensate
Q=-30.9 MeV
Q=+27.7 MeV
target system
projectile
Missing-mass spectroscopy
SHARAQ spectrometer
→ high resolution: ~ 1 MeV
2α detection at 200 MuV/u
→ good signal-to-noise ratio

22. Experimental Setup Primary Beam from Cyclotron (13.7 MHz)
Dispersive Focal Plane
・MWDC (Multi-Wire Drift Chamber)
momentum tagging for 8He beam
production
target F6 F3
High Resolution
Beam Line
・plastic scintillator
・micro hodoscope
start point of ion optics
・plastics scintillator
・MWDCs
target position
liq. He target
120 mg/cm2
φ=30 mm
FH9
8He beam α
liq. He target x
S2 focal plane S0 S0
SHARAQ
spectrometer S2
・plastic scintillator
・CRDCs
(Cathode Readout Drift Chamber)
two α tracking
Final Focal Plane

23. preliminary Result Missing-mass Spectrum of 4n
By Courtesy of K. Kisamori (RIKEN)
Result
preliminary
Missing-mass Spectrum of 4n
energy resolution: 1.2 MeV
uncertainty of calibration: ± 1.3 MeV
background: 2.3±1.0 events
→ almost background free
Candidate of the resonant state
clear strength with 4.9σ significance level
E4n = 0.83 ± 0.65 (stat.) ± 1.25 (syst.) MeV
upper limit of Γ = 2.6 MeV (FWHM)
cross section : nb
(int. up of θCM < 5.4 degree)
+2.9
-1.8

24. By Courtesy of K. Sekiguchi (Tohoku Univ.)

25. Chiral Effective Field Theory (CFT)
E. Epelbaum, Few-Body Syst. (2013) 54
Chiral EFT provides a systematic approach to nuclear forces which relies on the symmetries of QCD.
3NF naturally appear at N2LO.
Recently NN & 3NF at N3LO are constructed.

26. Faithful to Phase shift at asymptotic region
By Courtesy of T. Doi (RIKEN)
3NF from Lattice QCD
NBS wave function  Potential
Unified Contraction Algorithm (UCA)
Systematically reduce the huge computational cost
Faithful to Phase shift at asymptotic region
by 2N calc
S.Aoki et al. (HAL Coll.), PRD88(2013)014036
Doi-Endres CPC184(2013)117
(Wick)
(color/spinor)
x ~ 1000 for A=2  A=3
~ in our calc
Speed up by UCA
Speed up factor:

27. short-range repulsive 3NF !
By Courtesy of T. Doi (RIKEN)
Numerical Results
Triton channel
mp= GeV (mN= GeV)
T.D. et al. (HAL QCD Coll.) PTP127(2012)723
+ t-dep method updates etc.
short-range repulsive 3NF !
Preliminary
(cutoff artifact)
In progress/Prospects
Other geometries
Nf=2 clover (CP-PACS),
1/a=1.27GeV, L=2.5fm
Lighter mass w/ K-computer
3BF w/ hyperon (YNN/YYN/YYY)

28. 2-baryon forces (NN/YN/YY) at (almost) physical point
By Courtesy of T. Doi (RIKEN)
Breaking News
2-baryon forces (NN/YN/YY) at (almost) physical point
NN Tensor Force in 3S1-3D1
Clearly visible w/ physical mass !
Calc on K-computer in progress to improve S/N (& take larger t)
Preliminary
10PFlops
[HPCI Field5 Project 1]

29. Summary
3NF effect is one of the essential building blocks of the study of nuclear physics.
Highly precise Nd scattering data have been measured and allowed us to test the detail of 3NF models. -> Energy & spin dependencies are not good enough yet.
Theoretical progress in developing new 3NF potentials is highly expected.
More experimental studies are also expected. -> Massive & precise scattering data for parameter fittings -> New experiments for the study of 3NF (T=3/2) by using new experimental technique.